1. Field of the Invention
This invention relates in general to an adaptive equalization methods, and more particularly to adaptive equalization methods used with precoded systems dominated by inter-symbol interference (ISI).
2. Description of Related Art
Improvements in high-speed computers, networking equipment, and fiber optic technologies are bringing down the cost of building telecommunications facilities. While this trend began in the 1960s, more recent developments in wireless communications and high-speed digital services have broadened the capabilities of existing pipelines and created an appetite for lots of data. In fact, the appetite for data has outpaced the ability of existing networks to deliver it. One problem encountered by networks is intersymbol interference (ISI).
In intersymbol interference, the energy intended in one symbol spills over to the adjacent symbols. FIG. 1 illustrates intersymbol interference between received symbols 100. FIG. 1 illustrates 110 data sent from a transmitting device coupled to a non-ideal channel. The data 110 is divided into a plurality of symbols 112, 114, 116 dispersed over time in a manner so that adjacent symbols do not interfere with each other. Also illustrated in FIG. 1 is the data being received 120. The received data 120 is characterized by symbols 122, 124, 126 that have nonzero values 132, 134, 136 at an adjacent symbols sampling points.
To compensate for the amplitude and phase distortions introduced by the channel, equalizers are used. An equalizer is a discrete time filter for compensating these amplitude and phase distortions. A channel is a time-varying channel with a typically long time constant compared to the symbol period. The channel may be viewed as quasi-static, with a constant impulse response for the duration of a packet. The equalizer has to be adaptive to compensate continuously for nonidealities of the channel. A data packet may include a time-synchronization sequence, known as a training sequence, to derive the transfer characteristic of the channel at the time of transmission, and the data. The receiver then uses a signal processing algorithm to correct errors that occur in subsequent information bits.
FIG. 2 illustrates a typical digital communications system 200 in the presence of ISI. FIG. 2 illustrates a transition scheme for using a two-dimensional modulation. However, those skilled in the art will recognize that the invention and examples described herein are applicable to other types of modulation. Thus, FIG. 2 could be classified as a QAM, or a CAP system, with an in-phase and a quadrature components. FIG. 2 shows the in-phase and quadrature components in the transmitter at location A, where the upper path is the I channel 202 or in-phase and the bottom path is the Q channel 204 or quadrature phase.
Now, similarly in the receiver, in this particular drawing, at the summing node 210 to the right of the analog-to-digital converter (ADC) 212, there is an upper path 220 and a lower path 222. Again, the upper path 220 may be used to decode the in-phase component, and the lower path 222 may be used to equalize the quadrature component. So in each particular path, the signal first passes through the feed forward equalization block 230 of the DFE, and then to a direct DFE feedback loop 232. The DFE feedback loop includes a cross-coupled feedback loop 234. The direct feedback loop 232 will be from the I decision to the I summing node and the Q decision to the Q summing note. And then the cross-coupled components 234 will be from the I decision to the Q summing note, and from the Q decision to the I summing note.
In FIG. 2, the purpose of the feed forward equalizer (FFE) 230 is to cancel the maximum-phase response of the channel, which results in pre-cursor ISI. The purpose of the decision feedback equalizers (DFE) 232, 234 is to cancel the minimum-phase response of the channel, which results in post-cursor ISI. The equivalent channel response from point-A to point-B will be strictly minimum-phase and can be described as: EQU Y.sub.I =X.sub.I *H.sub.II +X.sub.Q *H.sub.QI Y.sub.Q =X.sub.Q *H.sub.QQ +X.sub.I *H.sub.IQ,
where the term X is used to denote the z-transform response X=X(z)=x.sub.0 +x.sub.1 z-.sup.1 +x.sub.2 z-.sup.2 + . . . , and the symbol * denotes the z-domain multiplication (time-domain convolution). H.sub.II refers to the channel response of the I channel input to the I channel output. H.sub.IQ refers to the channel response of the I channel input to the Q channel output. H.sub.QQ refers to the channel response of the Q channel input to the Q channel output. H.sub.QI refers to the channel response of the Q channel input to the I channel output.
The cross-coupled DFE 234, with coefficients 1-H.sub.II, -H.sub.IQ, 1-H.sub.QQ, and --H.sub.QI, is able to equalize the equivalent channel. Using adaptive algorithms driven to the correct solution by the decision error vector (i.e. RLS or LMS adaptation), the DFE can adapt to a correct solution from start-up, and also continuously adapt to equalize any changes in the channel response over time.
As shown in FIG. 2, no error correction coding is used. Therefore, preceding is not necessitated. Thus, the SNR seen at the decision node 240 would be quite high and the error rate would be very low. Now if there are any changes to the channel 250 over time, which would occur for changes in temperature or humidity, the feed forward equalizer 230 and the decision feedback equalizers 232, 234 would be able to handle any changes in the channel, since no equalization is performed in the transmitter other than transmit shaping.
However, the DFE is not the optimum solution if error control coding is utilized in the system, since error propagation in the feedback path and the requirement of accurate, immediate decisions for ISI subtraction both induce performance degradation when high gain error control is necessary.
To eliminate these problems, the minimum-phase response may be equalized by using transmitter-based equalizers, such as pre-emphasis, Tomlinson/Harashima precoder, and Laroia 151 precoder. The minimum-phase response equalization performed at the transmitter must first be trained at the receiver using an adaptive DFE to determine the filter coefficients 1-H.sub.II, -H.sub.IQ, 1-H.sub.QQ, and -H.sub.QI, and then transmitted to the receiver during some initialization start-up procedure.
FIG. 3 illustrates a typical precoded digital communications system 300. On the transmit side 310, data is passed through a convolutional encoder 320 and bits are mapped to symbols 322. In FIG. 3, Tomlinson/Harashima preceding 324 is illustrated prior to the digital-to-analog converter 326. However, any method of preceding may be used to illustrate the invention. The signal is then transmitted over the channel 328.
In FIG. 3, the DFE section is moved from the receiver into the transmitter. This is facilitated by the fact that low error rate decisions coming out of the error decision, which feed back into the ISI cancellation, are not needed. Instead, a completely ISI-free estimate could be produced and fed into an error correction decoder. Further, due to one incorrect decision causing multiple decisions immediately thereafter, completely freedom from any error propagation can be provided.
Turning to FIG. 3, again I 330, 340 and Q 332, 342 channels are shown. A standard Tomlinson precoder 324 is in the transmitter portion. Again, the DFE is cross-coupled 350. With regard to the receiver 312, the signal from the channel passes to analog-to-digital converter 360, which is split that into I 340 and Q 342 channels. Next, the same FFE 362 as described with reference to FIG. 2 receives the output of the summing node 364.
If after the FFE 362, there is no ISI left, i.e., the channel has not changed at all, then there is no need to have any type of a remaining DFE to cancel any post cursor ISI that may still exist. All that is needed is to take that output from the FFE 362 and send it into the decoder 366, and at the same time take the output of the FFE 362 and slice that to an extended decision 370, using an extended slicer, which is used with the Tomlinson precoder. That error 372 is used to update the FFE 362 and the echo cancellers 374.
However, if the channel does indeed change, and the output of the FFE 362 does contain some post-cursor ISI, the post-cursor ISI must be cancelled. This post-cursor ISI is cancelled through the use of the DFE 380 in conjunction with the Tomlinson precoder 324 in FIG. 3.
In summary, under perfect conditions where the channel 328 doesn't change, there is no need for the DFE 380 in conjunction with the Tomlinson precoder 324. Only the Tomlinson precoder 324 at the transmitter 310, and at the receiver 312 just the FFE 362 are needed, since the output of the FFE should be ISI free. However, once the channel 328 changes, the coefficients at the transmitter are locked in and thus can't be changed. So if the channel 328 changes, resulting ISI will occur which need to be cancelled. The DFE structure 380 in the receiver 312 allows the cancellation of this resulting ISI.
As suggested above, over time, the channel response may change due to temperature and humidity variation. For a 9kft, 26 AWO copper pair, termed Carrier Serving Area (CSA) Loop #6 from the T1E1.4 set of test loops, an isolated received pulse 400 for three temperatures 410, 412, 414 is shown in FIG. 4. For this case, there is approximately 10 dB of difference between the cold 410 and the hot 414 pulse amplitudes. Differences in the ISI vs. the main tap, which would yield different tap values, also exist. Any change in the maximum-phase response may be dealt with in the FFE by continuous adaptation based on the decision error vector. The minimum-phase response can not be directly and continuously adapted, since the fixed coefficients are now used in the transmitter, where the decision error vector is not available.
It can be seen that there is a need for an adaptive equalizer for adapting a precoder by generating updated coefficients for the precoder.
It can also be seen that there is a need for an adaptive equalizer that monitors the output of a DFE and compares it to a reference for updating a precoder in response to the comparison.